Issolvi 3x/5+4/x-2x/y=2

$$\frac { 3 x } { 5 } + \frac { 4 } { x } - \frac { 2 x } { y } = 2$$

Solvi għal y (complex solution)

$$y=-\frac{10x^{2}}{-3x^{2}+10x-20}$$

$$x\neq 0\text{ and }x\neq \frac{5+\sqrt{35}i}{3}\text{ and }x\neq \frac{-\sqrt{35}i+5}{3}$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli y ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'5xy, l-inqas denominatur komuni ta' 5,x,y.

$$xy\times 3x+5y\times 4-5x\times 2x=10xy$$

Immultiplika x u x biex tikseb x^{2}.

$$x^{2}y\times 3+5y\times 4-5x\times 2x=10xy$$

Immultiplika 5 u 4 biex tikseb 20.

$$x^{2}y\times 3+20y-5x\times 2x=10xy$$

Immultiplika x u x biex tikseb x^{2}.

$$x^{2}y\times 3+20y-5x^{2}\times 2=10xy$$

Immultiplika 5 u 2 biex tikseb 10.

$$x^{2}y\times 3+20y-10x^{2}=10xy$$

Naqqas 10xy miż-żewġ naħat.

$$x^{2}y\times 3+20y-10x^{2}-10xy=0$$

Żid 10x^{2} maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$x^{2}y\times 3+20y-10xy=10x^{2}$$

Ikkombina t-termini kollha li fihom y.

$$\left(x^{2}\times 3+20-10x\right)y=10x^{2}$$

L-ekwazzjoni hija f'forma standard.

$$\left(3x^{2}-10x+20\right)y=10x^{2}$$

Iddividi ż-żewġ naħat b'3x^{2}-10x+20.

$$\frac{\left(3x^{2}-10x+20\right)y}{3x^{2}-10x+20}=\frac{10x^{2}}{3x^{2}-10x+20}$$

Meta tiddividi b'3x^{2}-10x+20 titneħħa l-multiplikazzjoni b'3x^{2}-10x+20.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}$$

Il-varjabbi y ma jistax ikun ugwali għal 0.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}\text{, }y\neq 0$$

Solvi għal y

$$y=-\frac{10x^{2}}{-3x^{2}+10x-20}$$

$$x\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli y ma jistax ikun ugwali għal 0 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'5xy, l-inqas denominatur komuni ta' 5,x,y.

$$xy\times 3x+5y\times 4-5x\times 2x=10xy$$

Immultiplika x u x biex tikseb x^{2}.

$$x^{2}y\times 3+5y\times 4-5x\times 2x=10xy$$

Immultiplika 5 u 4 biex tikseb 20.

$$x^{2}y\times 3+20y-5x\times 2x=10xy$$

Immultiplika x u x biex tikseb x^{2}.

$$x^{2}y\times 3+20y-5x^{2}\times 2=10xy$$

Immultiplika 5 u 2 biex tikseb 10.

$$x^{2}y\times 3+20y-10x^{2}=10xy$$

Naqqas 10xy miż-żewġ naħat.

$$x^{2}y\times 3+20y-10x^{2}-10xy=0$$

Żid 10x^{2} maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$x^{2}y\times 3+20y-10xy=10x^{2}$$

Ikkombina t-termini kollha li fihom y.

$$\left(x^{2}\times 3+20-10x\right)y=10x^{2}$$

L-ekwazzjoni hija f'forma standard.

$$\left(3x^{2}-10x+20\right)y=10x^{2}$$

Iddividi ż-żewġ naħat b'3x^{2}-10x+20.

$$\frac{\left(3x^{2}-10x+20\right)y}{3x^{2}-10x+20}=\frac{10x^{2}}{3x^{2}-10x+20}$$

Meta tiddividi b'3x^{2}-10x+20 titneħħa l-multiplikazzjoni b'3x^{2}-10x+20.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}$$

Il-varjabbi y ma jistax ikun ugwali għal 0.

$$y=\frac{10x^{2}}{3x^{2}-10x+20}\text{, }y\neq 0$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{5}\left(\sqrt{y\left(40-7y\right)}+\sqrt{5}y\right)}{3y-10}\text{; }x=\frac{\sqrt{5}\left(-\sqrt{y\left(40-7y\right)}+\sqrt{5}y\right)}{3y-10}\text{, }&y\neq \frac{10}{3}\text{ and }y\neq 0\\x=2\text{, }&y=\frac{10}{3}\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=\frac{\sqrt{5y}\left(\sqrt{40-7y}+\sqrt{5y}\right)}{3y-10}\text{; }x=\frac{\sqrt{5y}\left(-\sqrt{40-7y}+\sqrt{5y}\right)}{3y-10}\text{, }&y\neq \frac{10}{3}\text{ and }y\leq \frac{40}{7}\text{ and }y>0\\x=2\text{, }&y=\frac{10}{3}\end{matrix}\right.$$